We explore the learning process and behavior of an individual with unrealistically high expectations (overconfidence) when outcomes also depend on an external fundamental that affects the optimal action. Moving beyond existing results in the literature, we show that the agent's beliefs regarding the fundamental converge under weak conditions. Furthermore, we identify a broad class of situations in which “learning” about the fundamental is self‐defeating: it leads the individual systematically away from the correct belief and toward lower performance. Due to his overconfidence, the agent—even if initially correct—becomes too pessimistic about the fundamental. As he adjusts his behavior in response, he lowers outcomes and hence becomes even more pessimistic about the fundamental, perpetuating the misdirected learning. The greater is the loss from choosing a suboptimal action, the further the agent's action ends up from optimal. We partially characterize environments in which self‐defeating learning occurs, and show that the decisionmaker learns to take the optimal action if, and in a sense only if, a specific non‐identifiability condition is satisfied. In contrast to an overconfident agent, an underconfident agent's misdirected learning is self‐limiting and therefore not very harmful. We argue that the decision situations in question are common in economic settings, including delegation, organizational, effort, and public‐policy choices.

A signal is privacy‐preserving with respect to a collection of privacy sets if the posterior probability assigned to every privacy set remains unchanged conditional on any signal realization. We characterize the privacy‐preserving signals for arbitrary state space and arbitrary privacy sets. A signal is privacy‐preserving if and only if it is a garbling of a reordered quantile signal . Furthermore, distributions of posterior means induced by privacy‐preserving signals are exactly mean‐preserving contractions of that induced by the quantile signal . We discuss the economic implications of our characterization for statistical discrimination, the revelation of sensitive information in auctions and price discrimination.

We characterize the set of extreme points of monotonic functions that are either majorized by a given function f or themselves majorize f and show that these extreme points play a crucial role in many economic design problems. Our main results show that each extreme point is uniquely characterized by a countable collection of intervals. Outside these intervals the extreme point equals the original function f and inside the function is constant. Further consistency conditions need to be satisfied pinning down the value of an extreme point in each interval where it is constant. We apply these insights to a varied set of economic problems: equivalence and optimality of mechanisms for auctions and (matching) contests, Bayesian persuasion, optimal delegation, and decision making under uncertainty.

We study how long‐lived, rational agents learn in a social network. In every period, after observing the past actions of his neighbors, each agent receives a private signal, and chooses an action whose payoff depends only on the state. Since equilibrium actions depend on higher‐order beliefs, it is difficult to characterize behavior. Nevertheless, we show that regardless of the size and shape of the network, the utility function, and the patience of the agents, the speed of learning in any equilibrium is bounded from above by a constant that only depends on the private signal distribution.

We study how an agent learns from endogenous data when their prior belief is misspecified. We show that only uniform Berk–Nash equilibria can be long‐run outcomes, and that all uniformly strict Berk–Nash equilibria have an arbitrarily high probability of being the long‐run outcome for some initial beliefs. When the agent believes the outcome distribution is exogenous, every uniformly strict Berk–Nash equilibrium has positive probability of being the long‐run outcome for any initial belief. We generalize these results to settings where the agent observes a signal before acting.

The expectation is an example of a descriptive statistic that is monotone with respect to stochastic dominance, and additive for sums of independent random variables. We provide a complete characterization of such statistics, and explore a number of applications to models of individual and group decision‐making. These include a representation of stationary monotone time preferences, extending the work of Fishburn and Rubinstein (1982) to time lotteries. This extension offers a new perspective on risk attitudes toward time, as well as on the aggregation of multiple discount factors. We also offer a novel class of non‐expected utility preferences over gambles which satisfy invariance to background risk as well as betweenness, but are versatile enough to capture mixed risk attitudes.

We study repeated independent Blackwell experiments; standard examples include drawing multiple samples from a population, or performing a measurement in different locations. In the baseline setting of a binary state of nature, we compare experiments in terms of their informativeness in large samples. Addressing a question due to Blackwell (1951), we show that generically an experiment is more informative than another in large samples if and only if it has higher Rényi divergences. We apply our analysis to the problem of measuring the degree of dissimilarity between distributions by means of divergences. A useful property of Rényi divergences is their additivity with respect to product distributions. Our characterization of Blackwell dominance in large samples implies that every additive divergence that satisfies the data processing inequality is an integral of Rényi divergences.